WASHINGTON (CNN) -- The Senate passed a new bill Thursday expanding a popular children's health insurance program, despite the lingering threat of a veto from President Bush.

President Bush speaks out Wednesday against legislation expanding a children's health care program.

The bill -- which boosts the number of low-income children covered by the State Children's Health Insurance Program -- was recently passed by the House, but without the veto-proof margin it received in the Senate.

Bush vetoed the first SCHIP bill and is expected to veto this one.

"There's a bill moving through Congress that's disguised as a bill to help children, but I think it's really a trick on the American people," the president said Wednesday.

The current program covers about 6 million children whose parents earn too much to qualify for Medicaid -- the federal health insurance program for the poor -- but who can't afford private insurance.

The new version would expand the program by nearly $35 billion over five years -- the same level as the previous bill, according to Democrats.

They want to extend the program to another 4 million children, paying for it with a 61-cent-per-pack increase in the federal tax on cigarettes.

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President Bush said the version he vetoed would have encouraged families to leave the private insurance market for the federally funded, state-run program.

He has proposed adding $5 billion to the program.

Thursday's Senate vote was 64-30, but several senators who have supported the bill were absent.

The Senate passed the earlier measure with the 67 votes needed to override a presidential veto.

Negotiations on a compromise bill are still under way, however, and there were encouraging words from two key senators involved in those talks.

Negotiators are close to an agreement on a measure, Senate Finance Committee Chairman Max Baucus, D-Montana, and Sen. Orrin Hatch, R-Utah, told reporters.

Hatch said he hoped the measure would be sufficiently different from the first two bills so Bush will want to sign it into law instead of vetoing it.

Talks will continue next week, Baucus said.

As of yet, none of the House Republicans who had been involved in the talks have signed on to compromise language, and the Senate will not return to the SCHIP bill until a compromise is reached, a Senate Democratic leadership aide said.

The House passed the bill last week on a 265-142 vote despite Republican complaints about holding the vote while several members were visiting wildfire-ravaged California districts.

Democratic leaders said the new version addresses Republican objections by tightening restrictions on illegal immigrants receiving SCHIP benefits; capping the income levels of families that qualify for the program; and preventing adults from receiving benefits.

But some Republicans weren't impressed.

Rep. Joe Barton of Texas last week compared the changes to "putting lipstick on a pig."

"It may a be a good pig. It may be a nice pig. It might be intended to be the right kind of pig," said Barton, the ranking Republican on the House Energy and Commerce Committee. "But it's still a pig."

And the White House said Bush would kill the new bill just as he had the last one.

"This bill does not address in a meaningful way the concerns the president raised, and so he will veto it if it reaches his desk," the White House said in a statement released after the House vote. E-mail to a friend